The Start

This is our standard, 2 fleet scenarios. There are 100 boats, 50 “large” (in blue) and 50 “small” (in black). The small boats have lower catchability, lower range and lower speed.
The biology layer is simple, there is a bunch of “biomass” at sea, growing logistically with more fishing growing further from port.

With no regulations the biomass is quickly depleted.

Why don’t we set a quota ?

Obvious solution to the over-catching problem is to set a maximum overall quota. The question is, how much should this yearly fleet-wide quota be? We find the answer with a straightforward 1-dimensional optimization, looking for the value that maximizes average profits.

While the average is good however, the fruits of this policy are shared unequally. Next we plot the yearly average profits split between large and small boats.

What is going on? Small boats can only fish inshore. In-shore fishing is however profitable for both fleets (since it consumes less gas and less travelling time). During the first years then both fleets focus on fishing near port, until that area is almost entirely depleted. Large boats then move out while small boats are left with almost nothing left to fish.
This is why even though the overall biomass is dropping, large boats’ profits continue to soar (until the very last years): they do not share the TAC with small boats anymore; the small boats are completely cut out.

Will tradeable quotas solve everything?

So far, this is just textbook policy-making. One common way to “fix” the inequality generated by the TAC is to parcel quotas out amongst boats and have them leasing to one another. This way small boats can still gain income by being “shareholders” of the fishery and profit from large boats higher efficiency.
Again we can run an optimization to figure out what’s the ITQ value that maximizes long term average profits.

And again we can study the profit dynamics for each class of boats.

Income for small boats starts higher but drops to low level after a few years. What’s going on?

Well, it all hinges on how the market for quotas evolves and in particular the intrinsic value small boats place on their quotas (which drive the price at which they are willing to lease them). Small boats are willing to lease their quotas only for more money than they would make by fishing themselves.
This works well initially, with small boats leasing quotas for a high price. However this quota is used by large boats to fish inshore (where it is most profitable).
Again, inshore biomass is consumed first. When inshore biomass is depleted the intrinsic value of quotas for small boats vanish: they can’t use it anymore for fishing since all the biomass is now out of range.
In a way, the bargaining power of small boats is eroded and they end up leasing quotas for very little money. Soon the sharing of profits start resembling the TAC case again.

Nothing completely unexpected but a neat little way to show how geography, agent heterogeneity and policy feed off each other.

Multiple Objective

Our quest is to both maximize efficiency (as landings or profits) and safeguard small boats income. This is a “multi-objective” optimization and we should treat it as such.

So imagine we swap our Bayesian optimizer for the NSGA-II algorithm, looking for the Pareto Front we can obtain when designing the ITQ. What we get is the following:

That is, with the ITQ we can increase small fishermen income slightly only by decreasing cumulative landings (that is, having smaller quotas). The idea is that if the total quota available is smaller you can keep the inshore biomass from collapsing immediately which strengthens the bargaining power of small boats when selling their quota.
The tradeoff is all concentrated around the Bayesian optimum we found before (the red cross in this graph).

Layering Policies

We figured out that small fishermen can only extract profits from the ITq market only as long as inshore biomass is still available to them as a fallback. The key idea then is to have two policies at once. An ITQ system and an inshore protected area that only small boats can access. This way the inshore biomass can be preserved for small boats as a fallback, increasing lease price of their quotas.

We run a 5-dimensional Pareto Front search (quota levels plus location, width and height of the MPA square) and we get the following.

That is, MPA+ITQ dominates ITQ alone. This makes obvious sense since we have more policy parameters, but it also makes sense in terms of dominance being almost entirely due to better outcome for small fishermen.
By guarranteeing a small-fishermen only area we can increase their income dramatically by strengthening their bargaining power, at no cost (and in fact slight benefit) to the overall efficiency.

Coping with cheating

What happens if we are in a situation where MPA boundaries are not easily enforceable?

Imagine that VMS is out of the question and large boats can only be caught with 10% probability when they fish in small boats only areas.
We can add that to the simulation and then recompute the best possible front, to see how much worse our solution space looks.

And now you see a much more pronounced tradeoff. First and foremost you see the Pareto Front shifting leftward (small fishermen suffer the most). This makes sense as the MPA is set up there to protect small fishermen and violations ruin inshore biomass and the bargaining power of small boats.

How do these solutions look like

We studied a bit the problem on the objective space, but it’s interesting to look at how the MPA+ITQ problem looks like in the fishery itself.